Good luck!
I'd go in positive, with a big smile on your face, and say "guess what, you're going to be a grandma!". If you are positive and upbeat, it leaves her less room to be judgemental and unhappy. Also, keep talking about how exciting it is, and how nervous you are, and how much you are looking forward to it, but you will need her help and advice. The more you talk, the more time she has to process it. And the more positive things you say will have an effect on her too. Then (if you can) start her talking about you (and your brothers and sisters) when you were a baby, that will keep her in nurturing mode, and she will want to take care of you again.
If you have a hang-dog expression, like you have something to apologise for, or be ashamned about, it will trigger her to give out to you more.
Trust me, she'll be fine. My brother got his girlfriend pregnant when they were both 17 with a boy, and again at 18 with a girl. Both sets of parents freaked both times for about a week, and then they were happy.
Babies always bring people together, even if it doesn't seem that way at first. 